I took the amtrak from Boston to NY twice in June for 2 diferent cruises from new york harbor. Amtrak runs a 6:20 am from Boston (you could board in providence, if you chose too) and arrives in Penn Station at 10:20 am. Took a cab to the pier and wa there by 11am. Very smooth. Cab ride from Penn Station about $6 one way.
If you leave the pier by cab at the end of your cruise, they distribute #'s, get one from the dispatcher and they call them in order, very organized. Hope this info helps.